Intermediate June 2019 Unit 2 Q10
10. Is it possible to draw a right-angled triangle with the measurements shown below?
You must use calculations (not a scale drawing) to support your answer.
You must show all your working. [4]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| Intent to square at least two of the three values. | S1 | (Note: 12·82 = 163·84, 22·72 = 515·29 and 25·62 = 655·36) |
| Comparing (25·6)2 with (12·8)2 + (22·7)2 or Any intent to compare any other relevant values. (e.g. (25·6)2 − (22·7)2 with (12·8)2 or √[(12·8)2 + (22·7)2] (with 25·6) ) | M1 | The comparison attempted must show both intended calculations e.g. (25·6)2 AND (12·8)2 + (22·7)2 unless intention is to compare with a given side e.g. √[(12·8)2 + (22·7)2] with 25·6 |
| Correct evaluation of value(s) to be compared. ( e.g ‘sight of 655·36 WITH 679·13’ or ‘sight of 140·07 WITH 163·84’ or ‘sight of 26·06 (WITH 25·6)’ ) | A1 | C.A.O. but allow evaluated answers to be given to the nearest whole number. e.g. 655 WITH 679. |
| Statement that it is NOT possible | A1 | Allow FT if M1 awarded. If all marks gained ISW. |
Alternative method 1
| Scheme | Marks | Comments | |||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Intent to use two right-angled trig ratios using 2 different pairs of given sides | S1 | i.e. In order to find the value of either the same angle OR two different angles, whilst sufficient to show that it isn’t a right-angled triangle. | |||||||||||||||||||||||||||||||||||
Correct right-angled trig ratio used twice, using 2 different given sides, in order to compare
| M1 | ||||||||||||||||||||||||||||||||||||
| Correct evaluation of value(s) to be compared. e.g. sight of any two of 30(°), 27.5…(°) and 29.4…(°) OR sight of 30(°) and 60.58…(°) (and the sum to be compared with 90°) | A1 | CAO
| |||||||||||||||||||||||||||||||||||
| Statement that it is NOT possible | A1 | If comparing the sum of two angles (with 90°), the sum must be shown. Allow FT if M1 awarded. If all marks gained ISW. |
Alternative method 2 (using the cosine rule)
| Scheme | Marks | Comments |
|---|---|---|
| NOTE The cosine rule is not on the intermediate tier specification, but as it is a common question, it may be seen by Higher tier candidates. | ||
| (cos A =) (12.82 + 22.72 – 25.62) / (2×12.8×22.7) (= 2377/58112 or 0·0409..) | M2 | M1 for 25.62 = 12.82 + 22.72 – 2×12.8×22.7×cos A |
| (A =) 87(.6557…°) | A1 | |
| Statement that it is NOT possible | A1 | If all marks gained ISW. |